Learn derivative at a point involves the process solving derivative problems at an exam point view. The rate of change of the given function is determined with the help of calculus. To find the rate of change the calculus is divided into two types such as differential calculus and integral calculus. At exam point of view the derivative is easily carried out by differentiating the given function with respect to input variable. The following are the solved example problems in derivatives at exam point of view for learn.
Learn derivative at a point example problems:
Example 1:
Find the derivative for the given differential function.
f(e) = 3e 3 -4 e 4 - 5e
Solution:
The given function is
f(e) = 3e 3 -4 e 4 - 5e
The above function is differentiated with respect to e to find the derivative
f '(e) = 3(3e 2 )-4(4e 3 ) - 5
By solving above terms
f '(e) = 9e 2 - 8e 3 - 5
Example 2:
Compute the derivative for the given differential function.
f(e) = 6e6 - 5 e5 - 4 e4 - e
Solution:
The given equation is
f(e) = 6e6 - 5 e5 - 4 e4 - e
The above function is differentiated with respect to e to find the derivative
f '(e) = 6(6e 5) -5 (5 e4 ) -4(4 e3) - 1
By solving above terms
f '(e) = 36e 5 - 25 e4 - 16 e3 - 1
Example 3:
Compute the derivative for the given differential function.
f(e) = 2e 2 -4 e 4 - 15
Solution:
The given function is
f(e) = 2e 2 -4e 4 - 15
The above function is differentiated with respect to e to find the derivative
f '(e) = 2(2e )-4(4 e 3 ) - 0
By solving above terms
f '(e) = 4e -16e3
Example 4:
Compute the derivative for the given differential function.
f(e) = 5e5 -4e 4 -3e 3 - 2
Solution:
The given function is
f(e) = 5e5 -4e 4 -3e 3 - 2
The above function is differentiated with respect to e to find the derivative
f '(e) = 5(5e 4 )-4(4e 3 ) -3( 3e 2) -0
By solving above terms
f '(e) = 25e 4 -16e 3 -9 e 2
Learn derivative at a point practice problems:
1) Compute the derivative for the given differential function.
f(e) = 2e 3 -3 e 4 - 4 e 5
Answer: f '(e) = 6e 2 -12 e3 - 20 e 4
2) Compute the derivative for the given differential function.
f(e) = e 3-e5 - 4 e 6
Answer: f '(e) = 3e2 - 5e4 - 24 e 5
Learn derivative at a point example problems:
Example 1:
Find the derivative for the given differential function.
f(e) = 3e 3 -4 e 4 - 5e
Solution:
The given function is
f(e) = 3e 3 -4 e 4 - 5e
The above function is differentiated with respect to e to find the derivative
f '(e) = 3(3e 2 )-4(4e 3 ) - 5
By solving above terms
f '(e) = 9e 2 - 8e 3 - 5
Example 2:
Compute the derivative for the given differential function.
f(e) = 6e6 - 5 e5 - 4 e4 - e
Solution:
The given equation is
f(e) = 6e6 - 5 e5 - 4 e4 - e
The above function is differentiated with respect to e to find the derivative
f '(e) = 6(6e 5) -5 (5 e4 ) -4(4 e3) - 1
By solving above terms
f '(e) = 36e 5 - 25 e4 - 16 e3 - 1
Example 3:
Compute the derivative for the given differential function.
f(e) = 2e 2 -4 e 4 - 15
Solution:
The given function is
f(e) = 2e 2 -4e 4 - 15
The above function is differentiated with respect to e to find the derivative
f '(e) = 2(2e )-4(4 e 3 ) - 0
By solving above terms
f '(e) = 4e -16e3
Example 4:
Compute the derivative for the given differential function.
f(e) = 5e5 -4e 4 -3e 3 - 2
Solution:
The given function is
f(e) = 5e5 -4e 4 -3e 3 - 2
The above function is differentiated with respect to e to find the derivative
f '(e) = 5(5e 4 )-4(4e 3 ) -3( 3e 2) -0
By solving above terms
f '(e) = 25e 4 -16e 3 -9 e 2
Learn derivative at a point practice problems:
1) Compute the derivative for the given differential function.
f(e) = 2e 3 -3 e 4 - 4 e 5
Answer: f '(e) = 6e 2 -12 e3 - 20 e 4
2) Compute the derivative for the given differential function.
f(e) = e 3-e5 - 4 e 6
Answer: f '(e) = 3e2 - 5e4 - 24 e 5
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